In the event that your application for a green card gets delayed, there are several actions you can take. Start by checking the application status through the USCIS website or calling customer service. If the delay exceeds what has been communicated to you, you may file a case inquiry or even request expedited processing in emergencies, like medical and other critical work reasons. 

When there has been a failure with your application due to some missing information or documents, go through your forms again to review if everything is in place. Some delays may be performed through filing of an appeal or motion to reopen for cases with correctable causes behind the delay.